Question

Ex 1 ,2 ,3 va rog frumos !

Answer 1

$\displaystyle \mathtt{E2.~~a) \left(\begin{array}{ccc}\mathtt{-1}&\mathtt4\\\mathtt2&\mathtt{-5}\\\end{array}\right)-\left(\begin{array}{ccc}\mathtt{-6}&\mathtt1\\\mathtt0&\mathtt2\\\end{array}\right)-\left(\begin{array}{ccc}\mathtt1&\mathtt0\\\mathtt0&\mathtt1\\\end{array}\right)=}$

$\displaystyle \mathtt{=\left(\begin{array}{ccc}\mathtt{(-1)-(-6)}&\mathtt{4-1}\\\mathtt{2-0}&\mathtt{(-5)-2}\\\end{array}\right)-\left(\begin{array}{ccc}\mathtt1&\mathtt0\\\mathtt0&\mathtt1\\\end{array}\right)=}$

$\mathtt{=\left(\begin{array}{ccc}\mathtt5&\mathtt3\\\mathtt2&\mathtt{-7}\\\end{array}\right)-\left(\begin{array}{ccc}\mathtt1&\mathtt0\\\mathtt0&\mathtt1\\\end{array}\right)=\left(\begin{array}{ccc}\mathtt{5-1}&\mathtt{3-0}\\\mathtt{2-0}&\mathtt{(-7)-1}\\\end{array}\right)=\left(\begin{array}{ccc}\mathtt4&\mathtt3\\\mathtt2&\mathtt{-8}\\\end{array}\right)}$

$\displaystyle \mathtt{\left(\begin{array}{ccc}\mathtt{-1}&\mathtt4\\\mathtt2&\mathtt{-5}\\\end{array}\right)-\left(\begin{array}{ccc}\mathtt{-6}&\mathtt1\\\mathtt0&\mathtt2\\\end{array}\right)-\left(\begin{array}{ccc}\mathtt1&\mathtt0\\\mathtt0&\mathtt1\\\end{array}\right)=\left(\begin{array}{ccc}\mathtt4&\mathtt3\\\mathtt2&\mathtt{-8}\\\end{array}\right)}$

$\displaystyle \mathtt{b) \left(\begin{array}{ccc}\mathtt{i^2}&\mathtt{-i^4}\\\mathtt2&\mathtt3\\\mathtt1&\mathtt{-1}\end{array}\right) +\left(\begin{array}{ccc}\mathtt1&\mathtt2\\\mathtt{-2}&\mathtt0\\\mathtt3&\mathtt4\end{array}\right)-\left(\begin{array}{ccc}\mathtt0&\mathtt i\\\mathtt{-3}&\mathtt2\\\mathtt4&\mathtt6\end{array}\right)=}$

$\displaystyle \mathtt{\left(\begin{array}{ccc}\mathtt{-1}&\mathtt{-1}\\\mathtt2&\mathtt3\\\mathtt1&\mathtt{-1}\end{array}\right) +\left(\begin{array}{ccc}\mathtt1&\mathtt2\\\mathtt{-2}&\mathtt0\\\mathtt3&\mathtt4\end{array}\right)-\left(\begin{array}{ccc}\mathtt0&\mathtt i\\\mathtt{-3}&\mathtt2\\\mathtt4&\mathtt6\end{array}\right)=}$

$\displaystyle \mathtt{=\left(\begin{array}{ccc}\mathtt{(-1)+1}&\mathtt{(-1)+2}\\\mathtt{2+(-2)}&\mathtt{3+0}\\\mathtt{1+3}&\mathtt{(-1)+4}\end{array}\right)-\left(\begin{array}{ccc}\mathtt0&\mathtt i\\\mathtt{-3}&\mathtt2\\\mathtt4&\mathtt6\end{array}\right)=}$

$\displaystyle \mathtt{=\left(\begin{array}{ccc}\mathtt0&\mathtt1\\\mathtt0&\mathtt3\\\mathtt4&\mathtt3\end{array}\right)-\left(\begin{array}{ccc}\mathtt0&\mathtt i\\\mathtt{-3}&\mathtt2\\\mathtt4&\mathtt6\end{array}\right)=\left(\begin{array}{ccc}\mathtt{0-0}&\mathtt{1-i}\\\mathtt{0-(-3)}&\mathtt{3-2}\\\mathtt{4-4}&\mathtt{3-6}\end{array}\right)=\left(\begin{array}{ccc}\mathtt0&\mathtt{1-i}\\\mathtt3&\mathtt1\\\mathtt0&\mathtt{-3}\end{array}\right)}$

$\displaystyle \mathtt{\left(\begin{array}{ccc}\mathtt{i^2}&\mathtt{-i^4}\\\mathtt2&\mathtt3\\\mathtt1&\mathtt{-1}\end{array}\right) +\left(\begin{array}{ccc}\mathtt1&\mathtt2\\\mathtt{-2}&\mathtt0\\\mathtt3&\mathtt4\end{array}\right)-\left(\begin{array}{ccc}\mathtt0&\mathtt i\\\mathtt{-3}&\mathtt2\\\mathtt4&\mathtt6\end{array}\right)=\left(\begin{array}{ccc}\mathtt0&\mathtt{1-i}\\\mathtt3&\mathtt1\\\mathtt0&\mathtt{-3}\end{array}\right)}$

$\displaystyle \mathtt{E3.~~A=\left(\begin{array}{ccc}\mathtt{-1}&\mathtt2&\mathtt0\\\mathtt1&\mathtt{-3}&\mathtt2\\\end{array}\right);~B=\left(\begin{array}{ccc}\mathtt1&\mathtt{-3}&\mathtt2\\\mathtt0&\mathtt{-1}&\mathtt2\\\end{array}\right);~C=\left(\begin{array}{ccc}\mathtt{-1}&\mathtt2\\\mathtt0&\mathtt3\\\mathtt{-4}&\mathtt{-5}\end{array}\right) }$

$\displaystyle\mathtt{a)A+B=?}\\\\\mathtt{A+B=\left(\begin{array}{ccc}\mathtt{-1}&\mathtt2&\mathtt0\\\mathtt1&\mathtt{-3}&\mathtt2\\\end{array}\right)+\left(\begin{array}{ccc}\mathtt1&\mathtt{-3}&\mathtt2\\\mathtt0&\mathtt{-1}&\mathtt2\\\end{array}\right)=}\\ \\ \mathtt{=\left(\begin{array}{ccc}\mathtt{(-1)+1}&\mathtt{2+(-3)}&\mathtt{0+2}\\\mathtt{1+0}&\mathtt{(-3)+(-1)}&\mathtt{2+2}\\\end{array}\right)=\left(\begin{array}{ccc}\mathtt0&\mathtt{-1}&\mathtt2\\\mathtt1&\mathtt{-4}&\mathtt4\\\end{array}\right)}$

$\displaystyle \mathtt{A+B=\left(\begin{array}{ccc}\mathtt0&\mathtt{-1}&\mathtt2\\\mathtt1&\mathtt{-4}&\mathtt4\\\end{array}\right)}$

$\displaystyle\mathtt{A-B=?}\\\\\mathtt{A-B=\left(\begin{array}{ccc}\mathtt{-1}&\mathtt2&\mathtt0\\\mathtt1&\mathtt{-3}&\mathtt2\\\end{array}\right)-\left(\begin{array}{ccc}\mathtt1&\mathtt{-3}&\mathtt2\\\mathtt0&\mathtt{-1}&\mathtt2\\\end{array}\right)=}\\\\\mathtt{=\left(\begin{array}{ccc}\mathtt{(-1)-1}&\mathtt{2-(-3)}&\mathtt{0-2}\\\mathtt{1-0}&\mathtt{(-3)-(-1)}&\mathtt{2-2}\\\end{array}\right)=\left(\begin{array}{ccc}\mathtt{-2}&\mathtt5&\mathtt{-2}\\\mathtt1&\mathtt{-2}&\mathtt0\\\end{array}\right)}$

$\displaystyle \mathtt{A-B=\left(\begin{array}{ccc}\mathtt{-2}&\mathtt5&\mathtt{-2}\\\mathtt1&\mathtt{-2}&\mathtt0\\\end{array}\right)}$